This invention relates an optical axis displacement sensor.
Recently, position-sensing apparatuses for measuring the displacement of a surface have been developed for loading numerical data representing a three-dimensional free-form surface having a complicated shape. These apparatuses can be classified into two types. The first type measures the distance to a surface by use of the principle of triangulation. The second type has a photoelectric converter and can be moved by a servo mechanism. The photoelectric converter detects the displacement of an image of a surface which has resulted from the displacement the surface with respect to a reference point. The apparatus is then moved by a servo mechanism until the displacement of the image is compensated, and finds the position of the surface from the distance it has been moved.
FIG. 6 shows a conventional apparatus of the first type. The apparatus has angle detector 12. Detector 12 comprises calibrating disk 11, and has a telescope, a slit plate and a photoelectric converter, all attached to disk 11. A laser beam emitted from a laser (not shown) is reflected at point P on surface S, and is incident onto angle detector 12. When surface S is shifted for distance .DELTA.z along the laser beam emitted from the laser, the angle of reflection of the beam varies. The angular variation .DELTA..theta. detected by detector 12 is given as: EQU .DELTA..theta.=.DELTA.z.multidot.sin .phi./R (1)
where .phi. represents the angle of an incident laser beam with respect to a line joining point P, before displacement, with the center of disk 11, and R represents the distance between point P, before displacement, and the center of disk 11.
When variation .DELTA..theta. is obtained by detector 12, displacement .DELTA.z of surface S can be calculated by way of the above equation (1).
FIG. 7 shows a knife-edge type positioning sensor of the second conventional apparatus. Positioning sensor 14 has micro-mirror 3 for reflecting a slightly diverged laser beam onto the optical axis of convex lens 2, knife-edge shielding plate 15 having a knife edge perpendicularly crossing the optical axis, at an image point Q of a point P, and photodetecting diodes 16a, 16b positioned symmetrically with respect to a plane defined by the optical axis and the knife edge. Sensor 14 is moved by a servo mechanism (not shown), the distance travelled being detected.
The apparatus is so adjusted that, when surface S is inclined in a plane including point P (i.e., when the image point is located at point Q), a differential output Ea-Eb of diodes 16a and 16b becomes zero. When surface S moves from the plane including point P, whereby the image point is shifted from point Q, part of the light incident on either one of diodes 16a and 16b is shielded by plate 15, so that the output Ea-Eb does not become zero. The servo mechanism moves sensor 14 such that the differential output becomes zero, and the degree of displacement from the plane including point P of surface S can be known by measuring the distance moved by sensor 14.
As can be understood from equation (1), in the apparatus of FIG. 6, .DELTA..theta. reaches its maximum when .phi. is .pi./2, provided .DELTA.z remains unchanged. Therefore, detector 12 should be so positioned that its detection face is perpendicular to the laser beam. In this case, however, a so-called "shadow effect" may occur wherein the light reflected from surface S is shielded by a projection protruding from detector 12 when surface S is shifted greatly as is shown in FIG. 8. Thus, a dead angle occurs, and the displacement of surface S cannot be correctly measured.
The knife-edge type sensor shown in FIG. 7 has the following drawbacks with regard to its incorporation in an optical system and the signal processing.
Plate 15 must be positioned at image point Q of point P in the optical system. To this end, the position of point Q must first be defined. As is apparent from the principle of reversibility, micro-mirror 3 must be designed and adjusted so as to reflect the beam applied from the light source and convert the beam to divergent light flux L represented by broken lines jointing point Q with some points on the surface of mirror 3. In other words, since the position of point Q (and hence point P) depends upon the optical system of the light source, the design, assembling and adjustment become complicated. Therefore, not only does the cost of the device increase, but it is also difficult to operate.
To eliminate such drawbacks, it is considered that point P depends upon the sole optical constant. For example, when parallel light beams are incident from a light source onto mirror 3, point P becomes the focal point of lens 2, and does not accordingly depend upon other optical constants. However, in this case, a new problem that image point Q (and hence the position of shielding plate 15) becomes infinitely remote.
As the rules of geometrical optics show, in the system of FIG. 7, no linearity exists between the positional changes of surface S and the that of image point Q. It is therefore difficult for a photoelectric converter to generate an output which quantitatively corresponds to the displacement of surface S. Since the light beams incident onto surface S are not parallel, the light-receiving area varies as surface S is displaced from the plane including point P, with the result that the size of the image alters, thereby giving rise to the drawback wherein the precise measurement of the displacement in a wide range is disabled.
Since the position of surface S where the differential output of diodes 16a and 16b becomes zero is located at point P, the absolute amount of light incident onto the diodes does not necessarily pose a problem with regard to signal processing. Hence, as long as the apparatus is used as a reference-pointing sensor, neither a variation in the incident energy of the diodes, generated by variations in the reflectivity of surface S and in the luminous intensity of the light source, nor an external disturbance such as an optical noise becomes a significant problem. In this sense, this apparatus is preferable, but another disadvantage of this apparatus resides in its employment of the servo mechanism. If the displacement of surface S is measured only with the apparatus in FIG. 7, without servo mechanism, the relationship between the displacement of surface S and the displacement of the image point becomes complicated. Since the measured result depends upon the difference of luminous quantities incident to diodes 16a and 16b, this apparatus has such disadvantages that the measured result cannot be obtained with reproducibility due to the difference in the reflectivity of surface S and the external disturbance.
Further, the other drawback of the apparatus in FIG. 7 is that, if surface S is not perpendicular to the optical axis, the apparatus does not correctly function. Since shielding plate 15 and diodes 16a, 16b correctly operate on the basis that the intensity distribution of lights incident from lens 2 to knife edge is symmetrical with respect to the optical axis, if surface S is inclined with respect to the optical axis, the intensity distribution of the reflected light does not become axis-symmetrical.